Mass Scaling Exponent Research Articles

Probing conformational properties of conjugated polymers in dilute solutions under variable solvent quality via coarse‐grained modeling

AbstractConjugated polymers (CPs), characterized by rigid conjugation backbones and flexible peripheral side chains, hold significant promise in various organic optoelectronic applications. In this study, we employ coarse‐grained molecular dynamics (CG‐MD) simulations to investigate the intricate interplay of solvent quality, temperature, and chain architecture (e.g., side‐chain length and molecular mass) on the conformational behaviors of CPs in dilute solutions. Our research uncovers distinctive conformational behaviors under varying solvent conditions, highlighting the versatile nature of polymer chains, which can adopt extended configurations in good solvents and transition to aggregated states in poor solvents. Additionally, the mass scaling exponent , a robust structural descriptor, consistently described CPs behavior across diverse architectures and solvent conditions. Furthermore, our study shows that a CP with longer side‐chain exhibits improved solubility, which is further confirmed by experimental observations. Moreover, our analysis of the shape descriptor provided valuable insights into the symmetry and dimensionality of CPs under varying solvent conditions. These findings offer a comprehensive understanding of conformational behaviors of CPs in dilute solution, which are helpful in guiding the conformational design of polymer for specific applications.

Standard metabolic rate differs between rainbow trout (Oncorhynchus mykiss) growth forms

In variable environments, repeatable phenotypic differences between individuals provide the variation required for natural selection. The pace-of-life syndrome (POLS) provides a conceptual framework linking individual physiology and life histories to behaviour, where rapidly growing individuals demonstrate higher rates of resting or “standard” metabolic rate (SMR). If differences in SMR are consistent between fast- and slow-growing individuals, these differences may be important to capture in bioenergetic relationships used to describe their growth, energy acquisition, and allocation. We compared growth rates and SMR between a domesticated and wild strain of rainbow trout ( Oncorhynchus mykiss (Walbaum, 1792)) using intermittent flow respirometry. Though mass-scaling exponents were similar between strains, mass-scaling coefficients of SMR for fast-growing rainbow trout were 1.25 times higher than those for slower growing fish. These observed differences in mass-scaling coefficients between fast- and slow-growing rainbow trout were consistent with data extracted from several other studies. Bioenergetic estimates of consumption for domestic strain fish increased as the difference in SMR and wild strain fish increased, and increased as activity level increased. Our results indicate patterns of SMR consistent with POLS, and suggest that strain-specific SMR equations may be important for applications to active populations (i.e., field observations).

Long-term effects of incubation temperature on growth and thermal physiology in a small ectotherm.

Thermal conditions in the developmental environment can substantially affect an individual's phenotype, particularly in egg-laying ectotherms. However, whether these effects persist into adulthood is rarely examined. To investigate this, we incubated delicate skink, Lampropholis delicata, eggs at either cool (22°C), mild (26°C) or hot (30°C) temperatures. After hatching, we measured growth, thermal performance curves of locomotor activity, and thermal sensitivity of resting metabolic rate of offspring as juveniles (4-6 weeks of age), sub-adults (approx. 200 days of age), and adults (approx. 2 years of age), and then measured developmental temperature impacts on male fertility. Incubation temperature had a lasting effect on growth and locomotor performance, with cool and hot incubation temperatures resulting in faster growth and larger maximum size, and hot incubation temperatures reducing locomotor performance at all timepoints. Effects on resting metabolic rate were only present in sub-adults, with a higher metabolic rate at high and average body mass and negative metabolic scaling exponent in cool-incubated lizards. Additionally, cool and hot incubation treatments resulted in shorter sperm midpieces and heads. Incubation temperature did not affect testis mass or sperm count. Overall, our results demonstrate that incubation temperature can have lasting effects on later life stages, highlighting the importance of maternal nest-site selection, but that some effects are age dependent. This article is part of the theme issue 'The evolutionary ecology of nests: a cross-taxon approach'.

Structure and conformational properties of ideal nanogel particles in athermal solutions.

We investigate the conformational properties of "ideal" nanogel particles having a lattice network topology by molecular dynamics simulations to quantify the influence of polymer topology on the solution properties of this type of branched molecular architecture. In particular, we calculate the mass scaling of the radius of gyration (Rg), the hydrodynamic radius, as well as the intrinsic viscosity with the variation of the degree of branching, the length of the chains between the branched points, and the average mesh size within these nanogel particles under good solvent conditions. We find competing trends between the molecular characteristics, where an increase in mesh size or degree of branching results in the emergence of particle-like characteristics, while an increase in the chain length enhances linear polymer-like characteristics. This crossover between these limiting behaviors is also apparent in our calculation of the form factor, P(q), for these structures. Specifically, a primary scattering peak emerges, characterizing the overall nanogel particle size. Moreover, a distinct power-law regime emerges in P(q) at length scales larger than the chain size but smaller than Rg of the nanogel particle, and the Rg mass scaling exponent progressively approaches zero as the mesh size increases, the same scaling as for an infinite network of Gaussian chains. The "fuzzy sphere" model does not capture this feature, and we propose an extension to this popular model. These structural features become more pronounced for values of molecular parameters that enhance the localization of the branching segments within the nanogel particle.

Effects of temperature on metabolic scaling in silver carp.

The association between temperature and metabolic scaling varies among species, which could be due to variation in the surface area and its scaling. This study aims to examine the effect of temperature on metabolic scaling and to verify the links between metabolic scaling and surface area scaling at both the whole body and the cell levels. The routine metabolic rate (RMR), gill surface area (GSA), ventilation frequency (VF), red blood cell surface area (SRBC ), and metabolic rate (MRRBC ) were determined in silver carp, and their mass-scaling exponents were analyzed at 10 and 25°C. These results showed that body mass and temperature independently affected the RMR, GSA, and VF, suggesting constant scaling exponents of RMR (0.772), GSA (0.912), and VF (-0.282) with changing temperature. The RMR at 25°C was 2.29 times higher than that at 10°C, suggesting increased metabolic demand at a higher temperature. The results showed that the RMR increased, while the scaling exponents of RMR, GSA, and VF remained unchanged with increasing temperature. These results support the view that the scaling of oxygen supply capacity importantly affects metabolic scaling. The SRBC did not change with either temperature or body mass. However, the MRRBC increased by 5.48 times from 10to 25°C but did not change with body mass. As the scaling exponents of RMR did not change between temperatures, the results indicate that no obvious link exists between the scaling of both the cell size and cell metabolic rate and the metabolic scaling of silver carp.

Temperature and mass scaling affect cutaneous and pulmonary respiratory performance in a diving frog.

Global climate change is altering patterns of temperature variation, with unpredictable consequences for species and ecosystems. The Metabolic Theory of Ecology (MTE) provides a powerful framework for predicting climate change impacts on ectotherm metabolic performance. MTE postulates that physiological and ecological processes are limited by organism metabolic rates, which scale predictably with body mass and temperature. The purpose of this study was to determine if different metabolic proxies generate different empirical estimates of key MTE model parameters for the aquatic frog Xenopus laevis when allowed to exhibit normal diving behavior. We used a novel methodological approach in combining a flow-through respirometry setup with the open-source Arduino platform to measure mass and temperature effects on 4 different proxies for whole-body metabolism (total O2 consumption, cutaneous O2 consumption, pulmonary O2 consumption, and ventilation frequency), following thermal acclimation to one of 3 temperatures (8°C, 17°C, or 26°C). Different metabolic proxies generated different mass-scaling exponents (b) and activation energy (EA ) estimates, highlighting the importance of metabolic proxy selection when parameterizing MTE-derived models. Animals acclimated to 17°C had higher O2 consumption across all temperatures, but thermal acclimation did not influence estimates of key MTE parameters EA and b. Cutaneous respiration generated lower MTE parameters than pulmonary respiration, consistent with temperature and mass constraints on dissolved oxygen availability, SA:V ratios, and diffusion distances across skin. Our results show that the choice of metabolic proxy can have a big impact on empirical estimates for key MTE model parameters.

Modeling short-chain branched polyethylenes in dilute solution under variable solvent quality conditions: Basic configurational properties

We perform molecular dynamics (MD) simulations of a coarse-grained model of linear low-density polyethylenes (LLDPEs) having short-chain branching in an implicit solvent and calculate basic configurational properties (radius of gyration Rg, hydrodynamic radius Rh, and intrinsic viscosity [η]) using the path-integration program ZENO. Solvent quality effects in our model are accounted for through the introduction of an attractive polymer-polymer interaction potential with solvent quality “strength” λ that is tuned from a “good” solvent limit, where the inter-polymer interactions are purely repulsive, to a “very poor” solvent regime, where the polymers collapse due to their self-attractive intermolecular interactions. We also identify a compensation condition or “θ point” in our model between these limits, where the polymers are “ideal” in the sense in which attractive interactions effectively nullify inter-polymer repulsions so that the chains behave akin to Gaussian polymer chains in their average conformational properties. In order to compare with experiments performed under variable solvent conditions, we define a dimensionless measure of excluded volume interaction parameter δ in terms of the mass scaling exponent ν for Rg or νh for Rh, which can be determined from both experiment and simulation. We illustrate our variable solvent approach to estimate polymer solution properties in the case of polyethylenes (PEs) and evaluate the δ value that corresponds to the experimental solvent conditions. Our combined use of MD and ZENO allows for the numerical estimation of polymer solution properties for polymers having general monomer structures and solvent qualities in a computationally tractable fashion and should be useful as a general computational tool for polymer structural characterization.

First estimates of metabolic rate in Atlantic bluefin tuna larvae.

Atlantic bluefin tuna is an iconic scombrid species with a high commercial and ecological value. Despite their importance, many physiological aspects, especially during the larval stages, are still unknown. Metabolic rates are one of the understudied aspects in scombrid larvae, likely due to challenges associated to larval handling before and during respirometry trials. Gaining reliable estimates of metabolic rates is essential to understand how larvae balance their high growth needs and activity and other physiological functions, which can be very useful for fisheries ecology and aquaculture. This is the first study to (a) estimate the relationship between routine metabolic rate (RMR) and larval dry weight (DW) (mass scaling exponent) at a constant temperature of 26°C, (b) measure the RMR under light and darkness and (c) test whether the interindividual differences in the RMR are related to larval nutritional status (RNA/DNA and DNA/DW). The RMR scaled nearly isometrically with body size (b = 0.99, 0.60-31.56 mg DW) in contrast to the allometric relationship observed in most fish larvae (average b = 0.87). The results show no significant differences in larval RMR under light and darkness, suggesting similar larval activity levels in both conditions. The size explained most of the variability in RMR (97%), and nutritional condition was unrelated to the interindividual differences in routine metabolism. This is the first study to report the metabolic rates of Atlantic bluefin tuna larvae and discuss the challenges of performing bioenergetic studies with early life stages of scombrids.

The combined effect of body size and temperature on oxygen consumption rates and the size-dependency of preferred temperature in European perch Perca fluviatilis.

The present study determined the effect of body mass and acclimation temperature (15-28°C) on oxygen consumption rate (ṀO2 ) and the size dependency of preferred temperature in European perch Perca fluviatilis. Standard metabolic rate (SMR) scaled allometrically with body mass by an exponent of 0.86, and temperature influenced SMR with a Q10 of 1.9 regardless of size. Maximum metabolic rate (MMR) and aerobic scope (MMR-SMR) scaled allometrically with body mass by exponents of 0.75-0.88. The mass scaling exponents of MMR and aerobic scope changed with temperature and were lowest at the highest temperature. Consequently, the optimal temperature for aerobic scope decreased with increasing body mass. Notably, fish <40 g did not show a decrease aerobic scope with increasing temperature. Factorial aerobic scope (MMR × SMR-1 ) generally decreased with increasing temperatures, was unaffected by size at the lower temperatures, and scaled negatively with body mass at the highest temperature. Similar to the optimal temperature for aerobic scope, preferred temperature declined with increasing body mass, unaffectedly by acclimation temperature. The present study indicates a limitation in the capacity for oxygen uptake in larger fish at high temperatures. A constraint in oxygen uptake at high temperature may restrict the growth of larger fish with environmental warming, at least if food availability is not limited. Furthermore, behavioural thermoregulation may be contributing to regional changes in the size distribution of fish in the wild caused by global warming as larger individuals will prefer colder water at higher latitudes and at larger depths than smaller conspecifics with increasing environmental temperatures.

Monitoring muscle over three orders of magnitude: Widespread positive allometry among locomotor and body support musculature in the pectoral girdle of varanid lizards (Varanidae).

There is a functional trade-off in the design of skeletal muscle. Muscle strength depends on the number of muscle fibers in parallel, while shortening velocity and operational distance depend on fascicle length, leading to a trade-off between the maximum force a muscle can produce and its ability to change length and contract rapidly. This trade-off becomes even more pronounced as animals increase in size because muscle strength scales with area (length2 ) while body mass scales with volume (length3 ). In order to understand this muscle trade-off and how animals deal with the biomechanical consequences of size, we investigated muscle properties in the pectoral girdle of varanid lizards. Varanids are an ideal group to study the scaling of muscle properties because they retain similar body proportions and posture across five orders of magnitude in body mass and are highly active, terrestrially adapted reptiles. We measured muscle mass, physiological cross-sectional area, fascicle length, proximal and distal tendon lengths, and proximal and distal moment arms for 27 pectoral girdle muscles in 13 individuals across 8 species ranging from 64g to 40kg. Standard and phylogenetically informed reduced major axis regression was used to investigate how muscle architecture properties scale with body size. Allometric growth was widespread for muscle mass (scaling exponent >1), physiological cross-sectional area (scaling exponent >0.66), but not tendon length (scaling exponent >0.33). Positive allometry for muscle mass was universal among muscles responsible for translating the trunk forward and flexing the elbow, and nearly universal among humeral protractors and wrist flexors. Positive allometry for PCSA was also common among trunk translators and humeral protractors, though less so than muscle mass. Positive scaling for fascicle length was not widespread, but common among humeral protractors. A higher proportion of pectoral girdle muscles scaled with positive allometry than our previous work showed for the pelvic girdle, suggesting that the center of mass may move cranially with body size in varanids, or that the pectoral girdle may assume a more dominant role in locomotion in larger species. Scaling exponents for physiological cross-sectional area among muscles primarily associated with propulsion or with a dual role were generally higher than those associated primarily with support against gravity, suggesting that locomotor demands have at least an equal influence on muscle architecture as body support. Overall, these results suggest that larger varanids compensate for the increased biomechanical demands of locomotion and body support at higher body sizes by developing larger pectoral muscles with higher physiological cross-sectional areas. The isometric scaling rates for fascicle length among locomotion-oriented pectoral girdle muscles suggest that larger varanids may be forced to use shorter stride lengths, but this problem may be circumvented by increases in limb excursion afforded by the sliding coracosternal joint.

Allometric models of adult regional body lengths and circumferences to height: Insights from a three-dimensional body image scanner.

Recent reports on body regional mass scalings to height have advanced understanding differences in adult heights. These studies resulted in conjectures on how regional lengths and circumferences may scale to height. We provide evidence for these conjectures by analyzing a large sample of regional limb, trunk, chest, and head lengths and circumferences in a large sample of US Army basic training recruits. Participants consisted of 10 271 males and 2760 females ages 17 to 21 years old who reported for basic training at Fort Jackson, SC. Participants were imaged by a three-dimensional (3D) body scanner for uniform sizing which yielded 159 body measurements of total mass, lengths and circumferences at regional sites of arms, legs, trunk, chest, and head. The allometric model, was applied to derive scaling exponents which were applied to estimate regional mass scalings. Body mass scaled to height with powers of ∼2.0 (mean β ± SE, 1.98 ± 0.04, 1.93 ± 0.06). Arm and leg lengths scaled to exponents larger than 1.0 and head height and circumferences at regional sites scaled to exponents smaller than 1.0. The leg, arm, and trunk mass scaling exponents were all above 2.0. Head mass scaled to powers smaller than 2.0. The 3D scanner allowed hundreds of anthropometric measurements to be obtained within seconds. The ensuing analysis revealed that greater height yielded disproportional increases in limb lengths, limb mass and trunk mass. These analyses provide evidence that could not be previously measured that further both biomechanical and metabolic conjectures.

Macroecology of fish community biomass – size structure: effects of invasive species and river regulation

The biomass of organisms of different sizes is increasingly being used to explore macroscale variation in food-web and community structure. Here we examine how invasive species and river flow regulation affect native fish biomass and fish community log10biomass – body mass scaling relationships in Australia’s largest river system, the Murray–Darling. The log10biomass – body mass scaling exponent (scaling B) of invasive fishes (95% CI: −0.14 to −0.18) was less negative than for native fishes (95% CI: −0.20 to −0.25), meaning that invasive species attained a higher biomass in larger size-classes compared to native species. Flow alteration and invasive common carp (Cyprinus carpio) biomass were correlated with severe reductions in native fish biomass ranging from −47% to −68% (95% CI). Our study provides novel evidence suggesting that invasive and native communities have different biomass – body mass scaling patterns, which likely depend on differences in their trophic ecology and body size distributions. Our results suggest that restoration efforts using environmental flows and common carp control has potential to boost native fish biomass to more than double the current level.

Differences in the respiratory response to temperature and hypoxia across four life-stages of the intertidal porcelain crab Petrolisthes laevigatus

For aquatic breathers, hypoxia and warming can act synergistically causing a mismatch between oxygen supply (reduced by hypoxia) and oxygen demand (increased by warming). The vulnerability of these species to such interactive effects may differ during ontogeny due to differing gas exchange systems. This study examines respiratory responses to temperature and hypoxia across four life-stages of the intertidal porcelain crab Petrolisthes laevigatus. Eggs, megalopae, juveniles and adults were exposed to combinations of temperatures from 6 to 18 °C and oxygen tensions from 2 to 21 kPa. Metabolic rates differed strongly across life-stages which could be partly attributed to differences in body mass. However, eggs exhibited significantly lower metabolic rates than predicted for their body mass. For the other three stages, metabolic rates scaled with a mass exponent of 0.89. Mass scaling exponents were similar across all temperatures, but were significantly influenced by oxygen tension (the highest at 9 and 14 kPa, and the lowest at 2 kPa). Respiratory responses across gradients of oxygen tension were used to calculate the response to hypoxia, whereby eggs, megalopae and juveniles responded as oxyconformers and adults as oxyregulators. The thermal sensitivity of the metabolic rates (Q10) were dependent on the oxygen tension in megalopae, and also on the interaction between oxygen tension and temperature intervals in adults. Our results thus provide evidence on how the oxygen tension can modulate the mass dependence of metabolic rates and demonstrate changes in respiratory control from eggs to adults. In light of our results indicating that adults show a good capacity for maintaining metabolism independent of oxygen tension, our study highlights the importance of assessing responses to multiple stressors across different life-stages to determine how vulnerability to warming and hypoxia changes during development.

Metabolic responses to temperature in a sedentary reef fish, the bluebanded goby (Lythrypnus dalli, Gilbert)

As climate continues to change, many marine species will experience both an increase in average temperature and more extreme diel and seasonal fluctuations. Understanding how these variations in ocean temperature affect processes such as metabolism and energy consumption is important for many species, and may be particularly important for sedentary species that cannot make large-scale movements in response to changes in environmental conditions. We examined how metabolic rates and energetic demands responded to temperature in a temperate reef fish, the bluebanded goby (Lythrypnus dalli). Using respirometry, we estimated resting oxygen consumption (VO2) for 42 L. dalli individuals of varying sizes and calculated metabolic rates (MR) at three different temperatures (13 °C, 16 °C, and 20 °C). As predicted, VO2 and MR increased significantly with temperature and mass, but the rate of temperature-dependent increase in metabolism indicated a very high degree of thermal sensitivity for L. dalli (Q10 value for VO2 was 5.21 across the range of experimental temperatures). The mass-scaling exponent (b) was estimated to be 0.95 and aligned closely with other benthic species. Our results suggest that changes in temperature – especially those that occur over weeks and seasons – likely play a significant role in the ecology of these gobies. Long-term increases in seawater temperature will either necessitate an increase in foraging and consumption, or drive costly trade-offs between metabolism and processes such as growth and reproduction.

Are the surface areas of the gills and body involved with changing metabolic scaling with temperature?

The metabolic-level boundaries (MLB) hypothesis proposes that metabolic level mediates the relative influence of surface area (SA)- versus volume-related metabolic processes on the body-mass scaling of metabolic rate in organisms. The variation in the scaling of SA may affect how metabolic level affects the metabolic scaling exponent. This study aimed to determine the influence of increasing metabolic level at a higher temperature on the metabolic scaling exponent of the goldfish and determine the link between metabolic scaling exponents and SA parameters of both gills and body. The SA of gills and body and the resting metabolic rate (RMR) of the goldfish were assessed at 15°C and 25°C, and their mass scaling exponents were analyzed. The results showed a significantly higher RMR, with a lower scaling exponent, in the goldfish at a higher temperature. The SA of the gills and the total SA of the fish (TSA) were reduced with the increasing temperature. The scaling exponent of RMR (bRMR) tended to be close to that of the TSA at a higher temperature. This suggests that temperature positively affects metabolic level but negatively affects bRMR The findings support the MLB hypothesis. The lower scaling exponent at a higher temperature can be alternatively explained as follows: the higher viscosity of cold water impedes respiratory ventilation and oxygen uptake and reduces metabolic rate more in smaller individuals than in larger individuals at lower temperature, thus resulting in a negative association between temperature and bRMR.

Mass scaling of metabolic rates in carabid beetles (Carabidae) - the importance of phylogeny, regression models and gas exchange patterns.

The origin of the allometric relationship between standard metabolic rate (MR) and body mass (M), often described as MR=aMb , remains puzzling, and interpretation of the mass-scaling exponent, b may depend on the methodological approach, shapes of residuals, coefficient of determination (r2) and sample size. We investigated the mass scaling of MRs within and between species of Carabidae beetles. We used ordinary least squares (OLS) regression, phylogenetically generalized least squares (PGLS) regression and standardized major axis (SMA) regression to explore the effects of different model-fitting methods and data clustering caused by phylogenetic clades (grade shift) and gas exchange patterns (discontinuous, cyclic and continuous). At the interspecific level, the relationship between MR and M was either negatively allometric (b<1) or isometric (b=1), depending on the fitting method. At the intraspecific level, the relationship either did not exist or was isometric or positively allometric (b>1), and the fit was significantly improved after the analyzed dataset was split according to gas exchange patterns. The studied species originated from two distinct phylogenetic clades that had different intercepts but a common scaling exponent (OLS, 0.61) that was much shallower than the scaling exponent for the combined dataset for all species (OLS, 0.71). The best scaling exponent estimates were obtained by applying OLS while accounting for grade shifts or by applying PGLS. Overall, we show that allometry of MR in insects can depend heavily on the model fitting method, the structure of phylogenetic non-independence and ecological factors that elicit different modes of gas exchange.

Temperature effects on mass-scaling exponents in colonial animals: a manipulative test.

Body size and temperature are fundamental drivers of ecological processes because they determine metabolic rates at the individual level. Whether these drivers act independently on individual-level metabolic rates remains uncertain. Most studies of intraspecific scaling of unitary organisms must rely on preexisting differences in size to examine its relationship with metabolic rate, thereby potentially confounding size-correlated traits (e.g., age, nutrition) with size, which can affect metabolic rate. Here, we use a size manipulation approach to test whether metabolic mass scaling and temperature dependence interact in four species (two phyla) of colonial marine invertebrates. Size manipulation in colonial organisms allows tests of how ecological processes (e.g., predation) affect individual physiology and consequently population- and community-level energy flux. Body mass and temperature interacted in two species, with one species exhibiting decreased and the other increased mass-scaling exponents with increasing temperature. The allometric scaling of metabolic rate that we observe in three species contrasts with the isometric scaling of ingestion rates observed in some colonial marine invertebrates. Thus, we suggest that the often observed competitive superiority of colonial over unitary organisms may arise because the difference between energy intake and expenditure increases more strongly with size in colonial organisms.

Ontogenetic body-mass scaling of nitrogen excretion relates to body surface area in diverse pelagic invertebrates

Many physiological and ecological processes depend on body size and the supply of limiting nutrients. Hence, it is important to derive quantitative predictions based on a mechanistic understanding of the influence of body size on metabolic rate and on the ratios of consumed to excreted elements. Among diverse pelagic invertebrates that change shape during ontogeny, recent analysis has demonstrated a significant positive correlation between the body-mass allometry of respiration rates (measured as the ontogenetic body mass-scaling exponent bR) and the allometry of body surface area (bA, as predicted from body-shape changes using a Euclidean model). As many pelagic invertebrates use a large portion of their external body surface for both resource uptake and waste excretion, we predicted that body-mass scaling exponents for rates of excretion of soluble N (bN) should also then relate to the degree of body-shape change during growth. We tested this hypothesis using literature data on bN for 39 species of pelagic invertebrates across five different phyla, and find strong support: bN is significantly positively correlated with predicted bA, whilst also co-varying with bR. Intraspecific differences between bN and bR values reveal ontogenetic shifts in the ratio of O2-consumed to N-excreted. We suggest that a variety of factors, including adaptive developmental shifts in the relative anabolism and catabolism of proteins and lipids, may cause these shifts in consumption–excretion ratios. Diverse pelagic invertebrates that dominate vast open water ecosystems falsify the predictions of general metabolic scaling theories built upon resource-transport networks, but support predictions of surface-area dependent theory.

Scalar field critical collapse in2+1dimensions

We carry out numerical experiments in the critical collapse of a spherically symmetric massless scalar field in 2+1 spacetime dimensions in the presence of a negative cosmological constant and compare them against a new theoretical model. We approximate the true critical solution as the $n=4$ Garfinkle solution, matched at the lightcone to a Vaidya-like solution, and corrected to leading order for the effect of $\Lambda<0$. This approximation is only $C^3$ at the lightcone and has three growing modes. We {\em conjecture} that pointwise it is a good approximation to a yet unknown true critical solution that is analytic with only one growing mode (itself approximated by the top mode of our amended Garfinkle solution). With this conjecture, we predict a Ricci-scaling exponent of $\gamma=8/7$ and a mass-scaling exponent of $\delta=16/23$, compatible with our numerical experiments.

Black hole critical behavior with the generalized BSSN formulation

The development of hyperbolic formulations of Einstein's equations has revolutionized our ability to perform long-time, stable, accurate numerical simulations of strong field gravitational phenomena. However, hyperbolic methods have seen relatively little application in one area of interest, type II critical collapse, where the challenges for a numerical code are particularly severe. Using the critical collapse of a massless scalar field in spherical symmetry as a test case, we study a generalization of the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation due to Brown that is suited for use with curvilinear coordinates. We adopt standard dynamical gauge choices, including 1+log slicing and a shift that is either zero or evolved by a Gamma-driver condition. With both choices of shift we are able to evolve sufficiently close to the black hole threshold to (1) unambiguously identify the discrete self-similarity of the critical solution (2) determine an echoing exponent consistent with previous calculations and (3) measure a mass scaling exponent, also in accord with prior computations. Our results can be viewed as an encouraging first step towards the use of hyperbolic formulations in more generic type II scenarios, including the as yet unresolved problem of critical collapse of axisymmetric gravitational waves.